1. Field of the Invention
The present invention relates to a signal processing device which serves to compute a phase difference between two alternating signals by a predetermined digital signal processing.
2. Description of the Related Art
U.S. Pat. No. 6,657,394 discloses an example of a signal processing device which serves to compute a phase difference between two alternating signals using digital signal processing technology. This kind of signal processing devices generally performs calculation based on the relations described below.
Assume that two alternating signals are expressed as V(θ)=sin(θ) and I(θ)=sin(θ−φ), where φ is the phase difference between the two alternating signals. Then, sin(φ) and cos(φ), which are obviously functions of φ, are derived from Formulae 7 and 8 shown below:
                                                                        cos                ⁡                                  (                  ϕ                  )                                            =                                                                    cos                    ⁡                                          (                      θ                      )                                                        ⁢                                      cos                    ⁡                                          (                                              θ                        -                        ϕ                                            )                                                                      +                                                      sin                    ⁡                                          (                      θ                      )                                                        ⁢                                      sin                    ⁡                                          (                                              θ                        -                        ϕ                                            )                                                                                                                                              =                                                                                          V                      ′                                        ⁡                                          (                      θ                      )                                                        ⁢                                                            I                      ′                                        ⁡                                          (                      θ                      )                                                                      +                                                      V                    ⁡                                          (                      θ                      )                                                        ⁢                                      I                    ⁡                                          (                      θ                      )                                                                                                                              (        7        )                                                                                    sin                ⁡                                  (                  ϕ                  )                                            =                                                                    sin                    ⁡                                          (                      θ                      )                                                        ⁢                                      cos                    ⁡                                          (                                              θ                        -                        ϕ                                            )                                                                      -                                                      cos                    ⁡                                          (                      θ                      )                                                        ⁢                                      sin                    ⁡                                          (                                              θ                        -                        ϕ                                            )                                                                                                                                              =                                                                    V                    ⁡                                          (                      θ                      )                                                        ⁢                                                            I                      ′                                        ⁡                                          (                      θ                      )                                                                      -                                                                            V                      ′                                        ⁡                                          (                      θ                      )                                                        ⁢                                      I                    ⁡                                          (                      θ                      )                                                                                                                              (        8        )            where V′(θ) and I′(θ) are derivatives of V(θ) and I(θ), respectively.
Conventional signal processing devices to perform such kind of computation generally incorporate a computing circuit shown in FIG. 7. This computing circuit includes an oscillator 41, multipliers 42a, 42b, 42c, 42d, and digital low pass filters 43a, 43b, 43c, 43d. The oscillator 41 serves to generate two reference waves sin(θ) and cos(θ). The multipliers 42a-42d serve to multiply either sin(θ) or cos(θ), which is a reference wave produced by the oscillator 41, and either V sin(θ) or I sin(θ−φ), which is an input alternating signal, together. The digital low pass filters 43a-43d serve to eliminate high frequency components.
Each of the multipliers 42a-42d, more specifically, outputs the product of one of the combinations of the alternating voltage signals and the reference waves in the following way. The multiplier 42a multiplies the alternating voltage signal V sin(θ) by the reference wave sin(θ), and then outputs the obtained product V sin(θ)sin(θ) to the digital low pass filter 43a. The multiplier 42b multiplies the alternating voltage signal V sin(θ) by the reference wave cos(θ), and then outputs the obtained product V sin(θ)cos(θ) to the digital low pass filter 43b. The multiplier 42c multiplies the alternating voltage signal I sin(θ−φ) by the reference wave cos(θ), and then outputs the obtained product I sin(θ−φ)cos(θ) to the digital low pass filter 43c. The multiplier 42d multiplies the alternating voltage signal I sin(θ−φ) by the reference wave sin(θ), and then outputs the obtained product I sin(θ−φ)sin(θ) to the digital low pass filter 43d. 
In this way, four products are produced in the computing circuit. These products are utilized by latter circuits to compute sin(φ) and cos(φ), to compute tan−1(φ) therefrom, and finally to obtain phase difference φ.
At actual use of this kind of computing circuits, in general, the frequencies does not accord perfectly between an alternating signal V sin(θ) or I sin(θ−φ), which is sent from outside, and a reference wave sin(θ) or cos(θ), which is generated inside the computing circuit. Assuming ω be an angular velocity whereby θ=ωt holds, and Δω be a minute difference between the frequencies of them, the reference waves are now expressed by sin(ωt+Δωt) and cos(ωt+Δωt).
Taking the difference Δω between the frequencies into consideration, Product-to-Sum Identities of trigonometric functions transforms each of the products calculated by the multipliers 42a, 42b, 42c, and 42d into the following forms, respectively.
            V      ⁢                          ⁢              sin        ⁡                  (                      ω            ⁢                                                  ⁢            t                    )                    ⁢              sin        ⁡                  (                                    ω              ⁢                                                          ⁢              t                        +                          Δω              ⁢                                                          ⁢              t                                )                      =                  (                  V          2                )            ⁡              [                              sin            ⁡                          (                                                2                  ⁢                  ω                  ⁢                                                                          ⁢                  t                                +                                  Δω                  ⁢                                                                          ⁢                  t                                            )                                +                      cos            ⁡                          (                              Δω                ⁢                                                                  ⁢                t                            )                                      ]                        V      ⁢                          ⁢              sin        ⁡                  (                      ω            ⁢                                                  ⁢            t                    )                    ⁢              cos        ⁡                  (                                    ω              ⁢                                                          ⁢              t                        +                          Δω              ⁢                                                          ⁢              t                                )                      =                  (                  V          2                )            ⁡              [                              sin            ⁡                          (                                                2                  ⁢                  ω                  ⁢                                                                          ⁢                  t                                +                                  Δω                  ⁢                                                                          ⁢                  t                                            )                                +                      sin            ⁡                          (                              Δω                ⁢                                                                  ⁢                t                            )                                      ]                        I      ⁢                          ⁢              sin        ⁡                  (                                    ω              ⁢                                                          ⁢              t                        -            ϕ                    )                    ⁢              cos        ⁡                  (                                    ω              ⁢                                                          ⁢              t                        +                          Δω              ⁢                                                          ⁢              t                                )                      =                  (                  I          2                )            ⁡              [                              sin            ⁡                          (                                                2                  ⁢                  ω                  ⁢                                                                          ⁢                  t                                +                                  Δω                  ⁢                                                                          ⁢                  t                                -                ϕ                            )                                +                      sin            ⁡                          (                                                Δω                  ⁢                                                                          ⁢                  t                                ⁢                                                                  +                ϕ                            )                                      ]                        I      ⁢                          ⁢              sin        ⁡                  (                                    ω              ⁢                                                          ⁢              t                        -            ϕ                    )                    ⁢              sin        ⁡                  (                                    ω              ⁢                                                          ⁢              t                        +                          Δω              ⁢                                                          ⁢              t                                )                      =                  (                  I          2                )            ⁡              [                              sin            ⁡                          (                                                2                  ⁢                  ω                  ⁢                                                                          ⁢                  t                                +                                  Δω                  ⁢                                                                          ⁢                  t                                -                ϕ                            )                                +                      cos            ⁡                          (                                                Δω                  ⁢                                                                          ⁢                  t                                +                ϕ                            )                                      ]            
Through the transformation above, it is obvious that each of the four products contains a second harmonic component sin(2ωt) to the reference waves. Each of the digital low pass filters 43a, 43b, 43c, and 43d is provided at the downstream from the multipliers 42a, 42b, 42c, and 42d, respectively, to eliminate second harmonic components. Thus, each of the output terminals OUT1-OUT4 outputs a signal without a second harmonic component to the reference waves.
The above-described signal processing device for computation of phase difference has two disadvantages. The first is instability of computed results of phase difference φ. The computed results at the output terminals OUT1-OUT4 are very sensitive to a minute difference between the frequency of the reference wave generated by oscillator 41 and the frequency of the alternating signal input from outside. This fact causes the phase difference φ, obtained by Formulae 7 and 8, to be unstable. The second is slow computing speed. The above-described signal processing device requires the digital low pass filters 43a-43d provided at the downstream from the multipliers 42a-42d in order to eliminate second harmonic components to the reference waves. These digital low pass filters 43a-43d, however, demand a lot of time to execute filtering operation.